-local unconditional structure of Banach spaces
Partial unconditionality of weakly null sequences.
We survey a combinatorial framework for studying subsequences of a given sequence in a Banach space, with particular emphasis on weakly-null sequences. We base our presentation on the crucial notion of barrier introduced long time ago by Nash-Williams. In fact, one of the purposes of this survey is to isolate the importance of studying mappings defined on barriers as a crucial step towards solving a given problem that involves sequences in Banach spaces. We focus our study on various forms of ?partial...
Partially bounded sets of infinite width.
Perturbations of Schauder bases in the spaces C(K) and , p<1
p-Frames and Shift Invariant Subspaces of L...
Pointwise smoothness, two-microlocalization and wavelet coefficients.
In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces Cx0s,s', and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet coefficients. We...
Positive bases in ordered subspaces with the Riesz decomposition property
In this article we suppose that E is an ordered Banach space whose positive cone is defined by a countable family of positive continuous linear functionals on E, i.e. E₊ = x ∈ E | for each i, and we study the existence of positive (Schauder) bases in ordered subspaces X of E with the Riesz decomposition property. We consider the elements x of E as sequences and we develop a process of successive decompositions of a quasi-interior point of X₊ which at each step gives elements with smaller support....
Primarité de
Produits tensoriels et , applications -sommantes, applications -radonifiantes
Projections de meilleure approximation continues dans certains espaces de Banach
Projections on Banach spaces with symmetric bases
Projetive generators and resolutions of identity in Banach spaces.
We introduce the notion of projective generator on a given Banach space. Weakly countably determined and dual spaces with the Radon Nikodým property have projective generators. If a Banach space has projective generator, then it admits a projective resolution of the identity. When a Banach space and its dual both have a projective generator then the space admits a shrinking resolution of the identity. These results include previous ones of Amir and Lindenstrauss, John and Zizler, Gul?ko, Vaak, Tacon,...
Properties of intersection in the geometry of sequences in Banach spaces.
p-trivial Banach spaces